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Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules.

Choubey S, Kondev J, Sanchez A - PLoS Comput. Biol. (2015)

Bottom Line: Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps.Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism.Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Brandeis University, Waltham, Massachusetts, United States of America.

ABSTRACT
Deciphering how the regulatory DNA sequence of a gene dictates its expression in response to intra and extracellular cues is one of the leading challenges in modern genomics. The development of novel single-cell sequencing and imaging techniques, as well as a better exploitation of currently available single-molecule imaging techniques, provides an avenue to interrogate the process of transcription and its dynamics in cells by quantifying the number of RNA polymerases engaged in the transcription of a gene (or equivalently the number of nascent RNAs) at a given moment in time. In this paper, we propose that measurements of the cell-to-cell variability in the number of nascent RNAs provide a mostly unexplored method for deciphering mechanisms of transcription initiation in cells. We propose a simple kinetic model of transcription initiation and elongation from which we calculate nascent RNA copy-number fluctuations. To demonstrate the usefulness of this approach, we test our theory against published nascent RNA data for twelve constitutively expressed yeast genes. Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps. Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism. Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.

No MeSH data available.


Related in: MedlinePlus

(A) Model of transcriptional regulation.The promoter switches between two states: an active and an inactive one. The probability per unit time of switching from the active state to the inactive state is kOFF, and from the inactive to the active state is kON. From the active state transcription initiation occurs in two sequential steps: the formation of the pre-initiation complex at the promoter proceeds with rate kLOAD after which the RNA polymerase escapes the promoter at a constant probability per unit time kESC. Once on the gene the polymerases move from one base pair to the next with a rate k, until they reach the end of the gene and they fall off with the same rate. From this model we compute the mean and the variance of the number of RNA polymerases, present on the gene in steady state, as a function of all the rates and the length of the gene L. This calculation is aided by introducing the mi variables for every base, which keep track of the number of polymerases at that base. (B) Noise profile for different models of transcription initiation. From the master equation of the model described in (A) we computed the Fano factor of the nascent RNA distribution as a function of the length of the gene being transcribed, for the three different models of transcription initiation: one-step (red), "bursty"(blue), and two-step initiation (black). The three different models give qualitatively distinct predictions. To illustrate this point for the "bursting" model we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, kLOAD= 5/min and kESC= 0/min, which are characteristic of the PDR5 promoter in yeast, as reported in [4]. For the two-step model we use kLOAD= 0.14/min, kESC= 0.14/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, characteristic of MDN1 promoter, which we find by analyzing the data reported in [25]. For the one-step model, we use kLOAD= 0.09/min, kESC= 0/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, which are characteristics of the yeast gene RPB1, obtained by analyzing the data published in [25]. (C) Noise profiles for different regulatory mechanisms. In the "bursting" model of transcription, the transcriptional output can be modulated either by changing the burst size or the burst frequency, which in the model can be achieved by tuning kOFF or kON. The Fano factor for the nascent RNA distribution obtained from burst size and burst frequency mechanisms of regulation are plotted as a function of the fold change in mean. (i.e., the mean of the distribution normalized by the maximum mean number of nascent RNAs in the cell, which is obtained when there is no transcriptional regulation and the promoter is always active). Clearly the two modes of regulation give qualitatively distinct predictions for the noise profile. (To illustrate this point we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, L = 4436 bps, kINI= 5/min, which were reported for the PDR5 promoter in yeast [4].)
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pcbi.1004345.g002: (A) Model of transcriptional regulation.The promoter switches between two states: an active and an inactive one. The probability per unit time of switching from the active state to the inactive state is kOFF, and from the inactive to the active state is kON. From the active state transcription initiation occurs in two sequential steps: the formation of the pre-initiation complex at the promoter proceeds with rate kLOAD after which the RNA polymerase escapes the promoter at a constant probability per unit time kESC. Once on the gene the polymerases move from one base pair to the next with a rate k, until they reach the end of the gene and they fall off with the same rate. From this model we compute the mean and the variance of the number of RNA polymerases, present on the gene in steady state, as a function of all the rates and the length of the gene L. This calculation is aided by introducing the mi variables for every base, which keep track of the number of polymerases at that base. (B) Noise profile for different models of transcription initiation. From the master equation of the model described in (A) we computed the Fano factor of the nascent RNA distribution as a function of the length of the gene being transcribed, for the three different models of transcription initiation: one-step (red), "bursty"(blue), and two-step initiation (black). The three different models give qualitatively distinct predictions. To illustrate this point for the "bursting" model we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, kLOAD= 5/min and kESC= 0/min, which are characteristic of the PDR5 promoter in yeast, as reported in [4]. For the two-step model we use kLOAD= 0.14/min, kESC= 0.14/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, characteristic of MDN1 promoter, which we find by analyzing the data reported in [25]. For the one-step model, we use kLOAD= 0.09/min, kESC= 0/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, which are characteristics of the yeast gene RPB1, obtained by analyzing the data published in [25]. (C) Noise profiles for different regulatory mechanisms. In the "bursting" model of transcription, the transcriptional output can be modulated either by changing the burst size or the burst frequency, which in the model can be achieved by tuning kOFF or kON. The Fano factor for the nascent RNA distribution obtained from burst size and burst frequency mechanisms of regulation are plotted as a function of the fold change in mean. (i.e., the mean of the distribution normalized by the maximum mean number of nascent RNAs in the cell, which is obtained when there is no transcriptional regulation and the promoter is always active). Clearly the two modes of regulation give qualitatively distinct predictions for the noise profile. (To illustrate this point we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, L = 4436 bps, kINI= 5/min, which were reported for the PDR5 promoter in yeast [4].)

Mentions: To describe the transcription initiation process we focus on promoter dynamics. (Here we use the term promoter to denote the stretch of regulatory DNA that controls the initiation of transcription of a specific gene.) The promoter switches between different states as different transcription factors bind and fall off their respective binding sites, causing the effective initiation rate to fluctuate. We assume that after initiation, each RNA polymerase (RNAP) moves along the gene by stochastically hopping from one to the next base at a constant probability per unit time (Fig 2A). Our model assumes that transcription initiation timescales are much slower than the elongation timescale and hence RNAPs do not interfere with each other while moving along the gene. This approximation is reasonable for all but the strongest promoters characterized by very fast initiation [43,44]. We demonstrate this explicitly using numerical simulations [45,46] which include a detailed model of transcription elongation that takes into account excluded-volume interaction between adjacent polymerases (i.e. “traffic” as defined in previous work [43]), as well as ubiquitous RNAP pausing [43,47] (please see S1A Fig). The agreement between analytical results based on our simple model and the stochastic simulations of the more realistic model that incorporates traffic jams and pausing of RNAPs only starts to break down when the initiation time scales become comparable to the elongation time scales (please see S1C and S1D Fig). We conclude that for typical rates reported for RNAP elongation and pausing the simple model of transcription adopted here reproduces the first two moments of the nascent RNA distribution with deviations from those obtained from the more realistic model that are less than 10% as long as initiation of transcription is slower than 30 initiations/min. All the initiation rates that have been reported so far from in vivo measurements are slower [4,19,23], with important exceptions such as the ribosomal promoters [43,44].


Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules.

Choubey S, Kondev J, Sanchez A - PLoS Comput. Biol. (2015)

(A) Model of transcriptional regulation.The promoter switches between two states: an active and an inactive one. The probability per unit time of switching from the active state to the inactive state is kOFF, and from the inactive to the active state is kON. From the active state transcription initiation occurs in two sequential steps: the formation of the pre-initiation complex at the promoter proceeds with rate kLOAD after which the RNA polymerase escapes the promoter at a constant probability per unit time kESC. Once on the gene the polymerases move from one base pair to the next with a rate k, until they reach the end of the gene and they fall off with the same rate. From this model we compute the mean and the variance of the number of RNA polymerases, present on the gene in steady state, as a function of all the rates and the length of the gene L. This calculation is aided by introducing the mi variables for every base, which keep track of the number of polymerases at that base. (B) Noise profile for different models of transcription initiation. From the master equation of the model described in (A) we computed the Fano factor of the nascent RNA distribution as a function of the length of the gene being transcribed, for the three different models of transcription initiation: one-step (red), "bursty"(blue), and two-step initiation (black). The three different models give qualitatively distinct predictions. To illustrate this point for the "bursting" model we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, kLOAD= 5/min and kESC= 0/min, which are characteristic of the PDR5 promoter in yeast, as reported in [4]. For the two-step model we use kLOAD= 0.14/min, kESC= 0.14/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, characteristic of MDN1 promoter, which we find by analyzing the data reported in [25]. For the one-step model, we use kLOAD= 0.09/min, kESC= 0/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, which are characteristics of the yeast gene RPB1, obtained by analyzing the data published in [25]. (C) Noise profiles for different regulatory mechanisms. In the "bursting" model of transcription, the transcriptional output can be modulated either by changing the burst size or the burst frequency, which in the model can be achieved by tuning kOFF or kON. The Fano factor for the nascent RNA distribution obtained from burst size and burst frequency mechanisms of regulation are plotted as a function of the fold change in mean. (i.e., the mean of the distribution normalized by the maximum mean number of nascent RNAs in the cell, which is obtained when there is no transcriptional regulation and the promoter is always active). Clearly the two modes of regulation give qualitatively distinct predictions for the noise profile. (To illustrate this point we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, L = 4436 bps, kINI= 5/min, which were reported for the PDR5 promoter in yeast [4].)
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pcbi.1004345.g002: (A) Model of transcriptional regulation.The promoter switches between two states: an active and an inactive one. The probability per unit time of switching from the active state to the inactive state is kOFF, and from the inactive to the active state is kON. From the active state transcription initiation occurs in two sequential steps: the formation of the pre-initiation complex at the promoter proceeds with rate kLOAD after which the RNA polymerase escapes the promoter at a constant probability per unit time kESC. Once on the gene the polymerases move from one base pair to the next with a rate k, until they reach the end of the gene and they fall off with the same rate. From this model we compute the mean and the variance of the number of RNA polymerases, present on the gene in steady state, as a function of all the rates and the length of the gene L. This calculation is aided by introducing the mi variables for every base, which keep track of the number of polymerases at that base. (B) Noise profile for different models of transcription initiation. From the master equation of the model described in (A) we computed the Fano factor of the nascent RNA distribution as a function of the length of the gene being transcribed, for the three different models of transcription initiation: one-step (red), "bursty"(blue), and two-step initiation (black). The three different models give qualitatively distinct predictions. To illustrate this point for the "bursting" model we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, kLOAD= 5/min and kESC= 0/min, which are characteristic of the PDR5 promoter in yeast, as reported in [4]. For the two-step model we use kLOAD= 0.14/min, kESC= 0.14/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, characteristic of MDN1 promoter, which we find by analyzing the data reported in [25]. For the one-step model, we use kLOAD= 0.09/min, kESC= 0/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, which are characteristics of the yeast gene RPB1, obtained by analyzing the data published in [25]. (C) Noise profiles for different regulatory mechanisms. In the "bursting" model of transcription, the transcriptional output can be modulated either by changing the burst size or the burst frequency, which in the model can be achieved by tuning kOFF or kON. The Fano factor for the nascent RNA distribution obtained from burst size and burst frequency mechanisms of regulation are plotted as a function of the fold change in mean. (i.e., the mean of the distribution normalized by the maximum mean number of nascent RNAs in the cell, which is obtained when there is no transcriptional regulation and the promoter is always active). Clearly the two modes of regulation give qualitatively distinct predictions for the noise profile. (To illustrate this point we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, L = 4436 bps, kINI= 5/min, which were reported for the PDR5 promoter in yeast [4].)
Mentions: To describe the transcription initiation process we focus on promoter dynamics. (Here we use the term promoter to denote the stretch of regulatory DNA that controls the initiation of transcription of a specific gene.) The promoter switches between different states as different transcription factors bind and fall off their respective binding sites, causing the effective initiation rate to fluctuate. We assume that after initiation, each RNA polymerase (RNAP) moves along the gene by stochastically hopping from one to the next base at a constant probability per unit time (Fig 2A). Our model assumes that transcription initiation timescales are much slower than the elongation timescale and hence RNAPs do not interfere with each other while moving along the gene. This approximation is reasonable for all but the strongest promoters characterized by very fast initiation [43,44]. We demonstrate this explicitly using numerical simulations [45,46] which include a detailed model of transcription elongation that takes into account excluded-volume interaction between adjacent polymerases (i.e. “traffic” as defined in previous work [43]), as well as ubiquitous RNAP pausing [43,47] (please see S1A Fig). The agreement between analytical results based on our simple model and the stochastic simulations of the more realistic model that incorporates traffic jams and pausing of RNAPs only starts to break down when the initiation time scales become comparable to the elongation time scales (please see S1C and S1D Fig). We conclude that for typical rates reported for RNAP elongation and pausing the simple model of transcription adopted here reproduces the first two moments of the nascent RNA distribution with deviations from those obtained from the more realistic model that are less than 10% as long as initiation of transcription is slower than 30 initiations/min. All the initiation rates that have been reported so far from in vivo measurements are slower [4,19,23], with important exceptions such as the ribosomal promoters [43,44].

Bottom Line: Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps.Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism.Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Brandeis University, Waltham, Massachusetts, United States of America.

ABSTRACT
Deciphering how the regulatory DNA sequence of a gene dictates its expression in response to intra and extracellular cues is one of the leading challenges in modern genomics. The development of novel single-cell sequencing and imaging techniques, as well as a better exploitation of currently available single-molecule imaging techniques, provides an avenue to interrogate the process of transcription and its dynamics in cells by quantifying the number of RNA polymerases engaged in the transcription of a gene (or equivalently the number of nascent RNAs) at a given moment in time. In this paper, we propose that measurements of the cell-to-cell variability in the number of nascent RNAs provide a mostly unexplored method for deciphering mechanisms of transcription initiation in cells. We propose a simple kinetic model of transcription initiation and elongation from which we calculate nascent RNA copy-number fluctuations. To demonstrate the usefulness of this approach, we test our theory against published nascent RNA data for twelve constitutively expressed yeast genes. Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps. Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism. Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.

No MeSH data available.


Related in: MedlinePlus